On the structural stability for a model of mixture of porous solids

Abstract

The present paper is dedicated to the structural stability of the linear model of a mixture of two porous solids. It is shown that the variation of the characteristic coefficients that describe the coupling of the various mechanical effects involved in the model in concern does not destroy its structure. This means that any small variation of these coefficients leads to small variations in the corresponding solutions of the associated initial boundary value problems. For this purpose, more mathematical estimates are presented describing precisely the continuous dependence of the solutions with respect to all external given data of the initial boundary value problem, as well as with respect to appropriate measures of the set of coupling parameters. This allows the conclusion that the model of the mixture of porous materials is consistent. In particular, it is believed that the estimates obtained in terms of structural stability are particularly meaningful with regard to the materials used in building contexts and the related decay phenomena.